{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.stattools import acf, pacf\n",
    "from statsmodels.tsa.arima_model import ARIMA\n",
    "from datetime import datetime, timedelta\n",
    "register_matplotlib_converters()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate Some Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $y_t = 50 + 0.4\\varepsilon_{t-1} + 0.3\\varepsilon_{t-2} + \\varepsilon_t$\n",
    "# $\\varepsilon_t \\sim N(0,1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "errors = np.random.normal(0, 1, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "date_index = pd.date_range(start='9/1/2019', end='1/1/2020')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 50\n",
    "series = []\n",
    "for t in range(1,len(date_index)+1):\n",
    "    series.append(mu + 0.4*errors[t-1] + 0.3*errors[t-2] + errors[t])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "series = pd.Series(series, date_index)\n",
    "series = series.asfreq(pd.infer_freq(series.index))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1bbb09d94c8>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(series)\n",
    "plt.axhline(mu, linestyle='--', color='grey')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_corr(series, lag):\n",
    "    return pearsonr(series[:-lag], series[lag:])[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ACF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 10 artists>"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf_vals = acf(series)\n",
    "num_lags = 10\n",
    "plt.bar(range(num_lags), acf_vals[:num_lags])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PACF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 25 artists>"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pacf_vals = pacf(series)\n",
    "num_lags = 25\n",
    "plt.bar(range(num_lags), pacf_vals[:num_lags])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get training and testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_end = datetime(2019,12,30)\n",
    "test_end = datetime(2020,1,1)\n",
    "\n",
    "train_data = series[:train_end]\n",
    "test_data = series[train_end + timedelta(days=1):test_end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit ARIMA Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create the model\n",
    "model = ARIMA(train_data, order=(0,0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fit the model\n",
    "model_fit = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                  121\n",
      "Model:                     ARMA(0, 2)   Log Likelihood                -179.864\n",
      "Method:                       css-mle   S.D. of innovations              1.069\n",
      "Date:                Sun, 29 Mar 2020   AIC                            367.727\n",
      "Time:                        17:33:01   BIC                            378.910\n",
      "Sample:                    09-01-2019   HQIC                           372.269\n",
      "                         - 12-30-2019                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         50.0478      0.157    318.883      0.000      49.740      50.355\n",
      "ma.L1.y        0.3686      0.088      4.176      0.000       0.196       0.542\n",
      "ma.L2.y        0.2538      0.086      2.949      0.004       0.085       0.422\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "MA.1           -0.7261           -1.8474j            1.9850           -0.3096\n",
      "MA.2           -0.7261           +1.8474j            1.9850            0.3096\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "#summary of the model\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicted Model:\n",
    "# $\\hat{y}_t = 50 + 0.37\\varepsilon_{t-1} + 0.25\\varepsilon_{t-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get prediction start and end dates\n",
    "pred_start_date = test_data.index[0]\n",
    "pred_end_date = test_data.index[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get the predictions and residuals\n",
    "predictions = model_fit.predict(start=pred_start_date, end=pred_end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = test_data - predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1bbb0b50bc8>"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "plt.plot(series[-14:])\n",
    "plt.plot(predictions)\n",
    "\n",
    "plt.legend(('Data', 'Predictions'), fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Percent Error: 0.0053\n"
     ]
    }
   ],
   "source": [
    "print('Mean Absolute Percent Error:', round(np.mean(abs(residuals/test_data)),4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Squared Error: 1.8254981729090671\n"
     ]
    }
   ],
   "source": [
    "print('Root Mean Squared Error:', np.sqrt(np.mean(residuals**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
